Electrical analogue



A. -WOLF ET AL Oct. 2, 1951 ELECTRICAL ANALOGUE 7 Sheets-Sheet l Filed Dec. 15, 1947 k Nml/ MKURNOU G @agonia 5mm\ w E mo.

v INVENTORJ ALEXANDER WOLF BURTON D. LEE

A TTORNE Y Oct. 2,'1951 A. woLF ETAL I ELECTRICAL ANALOGUE Filed Dec. 15, 1947 7 Sheets-Sheet 2 A. woLF :TAL

O ct. 2,V 1951 ELECTRICA;d ANALocuE 7 Sheets-Sheet 5 Filed Dec. l5, 1947 any cus y /N vAs/oN mor/rs IN VEN TOR; ALEXANDER WOL BURTON D. LEE

A TTORNEY Oct. 2., 1951 A. woLF ETAL 2,569,817

l ELECTRICAL ANALOGUE Filed Deo. 15, 1947 7 Sheets-Sheet 4 F I6. Z

Moron omrn'n se: F/as. s c n ALEXANDER WOLF BURTON D. LEE

BY 62 i,

ATmR/VEY INVENTORS f Oct. 2, 1951 A. WOLF ETI' AL ELECTRICAL ANALOGUE 7 Sheets-Sheet 5 Filed Deo. 15, 1947 l l l l l J i INVENTORS. ALEXANDER woLF auRro/v D. LEE

ATTORNEY /REcT/o/v ANPL /F/ER RHEosmT AMPL/F/ER 7 Sheets-Sheet 6 -T/ME scALE A. vWOLFl ET AL ELECTRICAL AANALOGUE rorALL//vc oEv/cE INVENTORS ANDER WOLF v BURTON D. LEE BY l ATTORNEY ALEX CURRENT CONTROL Oct. 2, `1951 `Filed Dec.

oct. 2, 1951 A.wo|.1= En.. 2,569,817

ELECTRICAL ANALDGUE Filed Dec. 15, 1947 7 Sheets-Sheet '7 INVENToRs. 26B I as l ALEXANDER wo/ F L 1 Buero/v 0.155

Arron/v51( Patented Oct. 2, 1951 ELECTRICAL ANALOGUE Alexander Wolf una Bui-mn D. Lee, immuni,`

Tex., assignors to The Texas Company, New York, N. Y., a corporation of Delaware Application December 15, 1947, Serial No. 791,796

16 Claims.

where I is the current owing through the unitV of area of a section whose specific resistivity is p, and across which there isa voltage gradient gg am (a: is normal to the area).

Darcys law for the ow of iluids through porous media is Le v n x y 2) where V is the rate of ow of a fluid whose viscosity is p. through a unit area of a section having a permeability k, and across which there is a pressure gradient (z is normal to the area).

The two laws are identical when the reciprocal of speciilc resistivity, is made numerically equal to the ratio of permeability to viscosity, in which case iiuid flow becomes directly comparable to current flow and electrical potential becomes directly comparable to pressure.

Electricity, if it be likened to a moving iluid, is incompressible. Consequently Ohms law (Equation 1) may be combined with the equation of continuity for an uncompressed or incompressible fluid (i. e. one which does not suf-l fer change in volume). The equation can be expressed as follows. for the iiow of electricity 6x and y and 3;-0 h (3) where y and z are the coordinates of a three dtilliliensional space taken at right angles to each 0 er.

If Equations 1 and 3 are combined, the result is Laplaces equation. viz.

62E 62E 62E 35:-,- and -yz'and zz=0 (4) 'Ihis equation governs the flow of electricity in a homogeneous isotropic conducting medium, but in view of the analogy between the flow oi uid (which does not suier change in volume) in a porous media and the ilow of electricity in the conductor, it may be taken as governing such uid ows as well, i. e. the iiow of electricity is analogous to the flow of fluids if the fluid is considered either as incompressible or uncompressed.

There are a number of engineering problems involving the investigation of steady-state dy vnamic systems in which force distribution can v be expressed in terms of electrical potentials and in which Laplaces equation, as a practical approximation, may be considered as controlling. It has been proposed heretofore, to solve-some of these problems (particularly that involving iiuid flow in a porous medium) by constructing an electrical analogue. Such an analogue may take the form of a conductive model, say a pool of electrolyte, the shape of which is analogous to the system to be investigated, exterior forces operating upon the system being represented in the analogue by electrical potentials imposed across the model. The conductor of the model may be of the electronic type, i. e. a conductive solid. Electrons are introduced at one or more points in the model and displace freek electrons throughout the conductor, so that electrons are forced to move out at another point, with resultant current ow. The conductor may also be of the ionic type, say a pool of electrolyte or an electrolyte dispersed in a body of gel.\current iiow being dependent upon `the mobility of ions through the conductor, but with current flow and potential drop established in the conductor just as in the electronic conductors.

` In both typesof conductors, potentials and potential gradients may be, determined by means of probes in contact with the points in question and connected to a potential measuring device such as a galvanometer. However, the collection of data by such means heretofore has been f tedious and time consuming, with the result that electrical analogues for solution of problems of the type described have not been employed to the f ullest extent.

The exploitation of an oil or gas field may be accomplished either by the expansion of the gas and oil in the producing formation, by displacement of the gas and oil by another fluid. or by vsimultaneous expansion and displacement.

I Whenever the displacement of the oil or gas is` the controlling factor there arises the problem of mapping the progress of the boundary between the iluid in place and the displacing iluid. This problem is of particular interest in the operation of a `cycling project in a gas-condensate fieldv In such an operation "wet" gas may be produced from one or more wells which are commonlyv called extractionv or output wells.

liquid condensate is removed.` The "dry gas 'I'he wet gas is sent to a processing plant where v remaining after removal ofthe liquid condensate is injected back into the producing formation through one or more wells, called injection or vinput wells, both-to conserve the gas for future use and also tomaintain the pressure in the neld.` In such a cyclingfoperation it is essential to'anticipate the manner in which the dry gas will spread through` the field, because the ultimate recovery of wet gas, and therefore. of`

valuabler liquid products, depends largely on keeping the dry gas from breaking rinto the extraction wells until substantially complete production of wet gas has been achieved. It is thus necessary to know theshape of the boundary or fluid interface between the wet and the dry gas around the injection wells for various varrangements of wells and for various injection and extraction rates. so that, a scheme can be selected which willpostpone this break-through to the latest possible date while maintaining a given different known methods. The iirst of these .or similar colloidal substances.

A color tracer is added to the electrolytic system to permit visualobservation of the progress of the ions between the points of different electrical potential in the system. The color tracerr may be a hydrogen ion indicator, such as phenolphthalein, contained in the electrolyte solution,

f in whichcase the vnegative electrodes represent the fluid source or iniection wells in the corresponding ilow system `and the positive electrodes representthe extraction; wells. 'I'he advance of` negativei ions as revealed by a colorchange of the indicator correspondsy to the advancing uid interface in the producing formation. In place o f an'indicator a colored ion may be injected into the system at the electrode corresponding to the rate ofgextraction and thereby permit themaxi- J mum-recovery of wet gas.v After break-through 1 of dry gasinto an extraction well has occurred,

it then may be necessary todetermine theexpected proportion of dry gas which will be mixed with the wet 'gas produced by the well.

Exploitation problems ofv theV type described` above and the application of electrical analogues to the solution thereof are discussed by Muskat in his book The Flow of Homogeneous Fluids Through Porous Media." Unfortunately the mathematical solution of the type of problem outlined abovecan be carried out only for certain idealized arrangements of injection` and extractionwells and then only for the simplest or e boundary conditions. `The mathematical solution for the well arrangements and boundaries which are encountered in actual practice is entirely impractical because of the excessive labor involved. 'I'he only feasible approach to the solution of these problems is through the use of models on a reduced scale. These models need not actually employ a porous medium and a fluid. As pointed out above, there exists, with certain assumptions, an exact analogy between the ilow of fluid in a porous'medium and theilow of electrical ycurrent in a conducting` body of similar geometry."

If electrical currentsl proportional to rthe-rates of injection and extraction of fluid are passed through such a conductor by means of electrodes located at points corresponding yto the positions `of the wells in the held, then theelectrical potential distribution in the conductor is exactly analoinjection well. In such a case a colorless solution of zinc-ammonium chloride may be employed as the electrolyte in theporous medium' and a solution of copper-ammonium chloride may be injected at the positive' electrodes. The progress of the blue copper-ammonium ions from the positive to the negative electrodes corresponds to the advancing nuidinterface inthe formation. The progress of the equivalent` fluid interface may be observed and recorded by .making photographs of the positionl of the colored areas of the model at various time are begun. y l

The electrolytic model gives the desired results quite rapidly but with inferior accuracy due to a loss of sharpness of the boundaries of the fluid interface as the pattern spreads out. It has been shown that the total effect of the several inherent errors of the electrolytic method may result in an overall error of asmuch as 25% in the determination of the volume of the formation flooded by individual injection wells. In view of this the results obtained with theelectrolytic model are generally consideredto be of a qualitative nature or at best only semi-quantitative. A second method for carrying out such studies is by means of` the velectrical conduction or so-called potentiometric model. This model consists ordinarily of a pool of a conducting liquid, such as a dilute solution of copper sulphate in intervals ,after the experiments water. l'I'he bottom of the conducting pool is gous to the' fluid pressure distribution inthe field, i

v and the current -ilow lines correspond to the fluid shapedy such that the depth of the conducting liquid at any point corresponds to the actual quantity of oil or gas contained inthe producing sand at the corresponding point in the formation. The periphery of the conducting pool is shaped to correspond to the geometrical boundaries of the formation. The 4necessary information for `the. construction ofthe conducting pool is obtained from an isopachous map ofthe formation on whichthev contour lines of equal sand thicknow lines in the held. f The study of fluid flow in an oil field is thus reduced to a study of cur- 7 rent flow in an electrical conductor of suitable shapef In making studies on electrical models employl ness have converted to represent actual oil o content bycorrecting for sand volume and con- 4 various wells in the ileld vertical metallic elecamaai? 6 o trodes are introduced into the pool, usually with a rotatable head upon which a pair of cona through'the bottom so as not to interfere with tacts are fastened in spaced relationship. Simithe measurements. Through these electrodes larly the marker member is provided with a roelectric currents are passed into and out of the tatable head, provided with a pair of tracing pool, the flow of current being either into or points spaced to .correspond to the contacts, `the out of the pool depending upon whether the well axes of rotation of the two heads bearing similar represented is an injection or extraction well, relationships respectively .to the model and the and the magnitude of the currents being proporchart. The mechanical linkage is such that the tional to the uid injection and extraction rates two heads move in unison and correspondingly which are employed or which it is proposed to lo'respectively over model and chart and rotate employinthe exploitation of the field. Asalreadyv correspondingly so that when the contacts are.

equation. The Wolf apparatus comprises a three of-Fig 3;

mentioned, the direction of current flow at any.. onanequlpotential line in the model, with no point inthe conducting pool is therl`. identical,j l tential difference indicated by a galvanometer the direction of fluid now at the lcorrespondin onnected across them, a corresponding line will point in the oil-bearing formation, and the poten ndieated by the tracing points on the chart.

tial gradient at any point in the conducting poo `T lieii'ise of two or more contacts, with the pluis proportional to the pressure gradient at the ralitylormarkers permits equlpotential lines to corresponding point in the formation. Any .ele-` beplotted much more rapidly than when only ment of fluid in the formation follows a path singlejcontacts or probes with single markers are corresponding -to a current flow line in the con- 2o employed'.Moreover, if one set of markers is ducting pool and the transit time for such elee disposediat right angles to a-set of probes or conment of iluid from one point to another in the tactsbutarranged to rotate in unison thereformationisproportionaltothe line integral with, flow vlines may be plotted directly, with om y additional savings in time. l --Pdz l l We prefer toemploy a rotatable probe head having multiple contacts thereon, with a correta-ken alOng a 110W line in the formation, Where sponding rotatable marker head with multiple I iS the travel distance and P iS l911e Pressure markers. The marker headislinkedtothe probe Hence the transit time for any element of iluid head mechanically so kthat the two move roin the formatien 1S e150 Proportional t0 the line 3o spectively over model and chart in unison 'and integral also rotate in unison. Operations are simplified or if one contact and -one marker are disposed .at

fw I the respective axes of rotation of probe head and marker head.

taken along a current une m theconduc'ting The foregoing and other aspects of our in., Wnel'e x is tne corresponding travel distance in vention willy be understood completely in the light the PoelandViS'the Potential of the following detailed description, taken in The problem of mapping tlle progress or an conjunction with the accompanying drawings interface between the driving and the driven in which: l fluids is essentially the problem of determining 40 Fig i is a diagram of one form of the ennarm these integrals along all of the current lines in tus or our invention illustrating the linkage be, the electrically conducting pool. The potentiotween a rotatable probe heed heving e nairof merrie, method' however' nas not been employed contacts for locating equlpotential lines on a con'- extensively, because heretofore the means for ductive model end e rotatable marker-heed obtaining the line integrals have been too cumequipped with corresnonding trecing points'- for bersome for practical application. The method plotting such lines on e chart; which has been employed previouslyfor arriv- Fig 2 is a diagram similar to luie` l butillusing at nulo travel time by means or potentiotrating the plotting of flow lines on the chai-tat metric model studies is tedious and time consuml right aingles to equinotentiai linee explored in thev mgmodel;

Co-pending application Serial No. 791,797, filed Flg 3 is a perspective view of a `preferred en? December 12, Alexander discloses bodiment of the apparatus of the invention par; 'Y

and claims an apparatus nion greatly faollitates tlcularly adapted to the investigationl of oil eld the collection and utilization of data with elecproblems;` f

trical analogues of steady-state systemsthat are Fim 4 is e plan oye conductive model of an governed" at least approximately' by .'i-'aplaoe's 55 oil bearing formation for use with the apparatus dimensional electrically conductive model anal- Fig 5 is a partiel section through the model ogous to the system to be investigated, a chart of Fig' .i taken along the line 5 5;

(Say one corresponding to a plan of the model),v o Fig; s is an isopaohous map of 'me oil bearingV means for establishing across the model a current formation of Fig. 4, with gow lines thereon oonanalogous to rol'oe operating upontile System' 9' structed in accordance with theinventlon;

conductive probe disposed in contact with the Fig. 7 is e perspective view of the probe'merli'.V l

model, means fOr.. determining the potential 0f er head, and the mechanical linkage of thesetwo the probe, a marker disposed adjacent the chart, elements in the apparatus of Fig, 3; y

and a linkage connecting the marker `to the probe Fig- 3 is a diagram of `the circuit employed in i'or moving the marker on the chart to correspond the apparatus of Fig, 3 for manual operation;

to movements of the probe on the model. pig 9 is a diagram of the circuit employed in' In accordance with the instant invention et the circuit of Fig. 3 for automatic operation; and least two contacts are provided on the probe, Fig, 10 is a. diagram illustrating a time-'scale with COrIeSDOnding multiple tracing points 0n the 7o totaling device incorporated in the apparatus of marker, the linkage being such that the tracing Fig. 3; y

points move on the chart to correspond to the The apparatus of Fig. 1 is arranged for plotting movements of the contacts on the model. Thus, equlpotential lines. `It comprises an electrolvtic y for example, Iif it is desired to plot lines of equimodel 45 in the form of a basin of insulating ma'` potential in the model, the probe may be equipped terlal shaped to correspond to the system'under going investigation. say a wet gas lleld, and con--y taining a D001 oi' electrolyte. Electrodes I. l1. Ii.- ll. corresponding to extraction wells and an electrode le corresponding to an injection well. project into'the pool from the bottom and re-y ceive currentfrom a source Il.

A- probe head 52 is supported above the pool and. is-mounted to rotate on a vertical axis on one uid or a norizontalarm vin longitudinal slider 12A. "Ihe other end carries a marker head il.

likewise rotatable on avertical axis. A chart'or l through the contacts always parallel to a line through'the tracer points. Theprobe l! the corresponding tracer point 51 are disposed respectively on the axes of the pulleys.`so that their companion probeV or tracer point (as the case may be) rotates dMIOSedattheaxis.` y o The arm 52A is `slidable longitudinally yin a holder or lateral sliderV I0 whichy rests on a horizontal supporting rail 8| running at right angles around the member to' the arm. AThe holder slides along the rail, so

. that Vthe probe head may be moved to any portion of the pool with the marker head occupying af corresponding position above the chart. The tivo contacts are connected toa salvanomet'er Il, todetectxwhen they are ona line of equipo- -With the current flowing through the model,

vthe'probe head is rotated until vthe two contacts afreat thesame potential. The two markers `are then depressed to mark corresponding points in the chart. The probe head is then vmoved* until the contact El occupies the positionforlnerly ocoupiedby'the contact 5t and thenfthe'probe is rotated until both. contacts are `again "at the same potential, when the markers are vagain depressed. In this way a series of points on an equipotential'line are determined.r

`Theimpartan: 01mg. `2 is identical with that o'f Fig.' l."except that the line joining the tracing joints, 51, Il, is at rightjanglesrto that joining thejcontacts on the probe head.` Consequently "markers define a ilowline at right angles to fthe lequipotential line found by thefeontacts.

'when an equipotential line is thus found. the markers arey depressed to marl;` the chart. The marker head is then movedso that one marker point'occupieswthe position formerly occupied by the other; The probe head is then rotated until its contacts are onnanother equipotential line. when the marker head will have definedl a third point on theflow line, 'the joper'ation" beingre- `peateduntil tlleilowl'ine is plottedcompletely.

Referring to Fig'.- 3 of the drawings, a reducedscale model H0 `of an oil-bearing formation has a conducting pool ||2.` the geometry of which.

corresponds tothe geometry of the formation as deflnuedvby avcorrec'ted isopachousmap III. lOn atypical isopa'ehousmap the contour lines represent thetnitkness or .the oil-bearing strata, "rnc oil itself as well as some connate water, occupies thelnterstices or pores in theoil sand. In the corrected isopachous map .I Il, as-shown in Fig. 6,

thecontour lines I i6 represent the eii'ective thicknels-of the actual oil content at various points` in the formation after correction for the volume occupied by sand and water.'- Oil wells IIIA, HIB. HIC, IIID indicated on the' isopachous map ill (see Fig. 6) are represented in the model ||0 by nxed electrodes |20, preferably inserted t through the bottom of the model for convenience.

and projectinginto the conducting pool `i I2. By means ci' -a current control unit |22 electric currents are passed through lthe fixed electrodes and the conducting pool'. the magnitude of the n currents bearing a direct relationship to actual or investigated rates of extraction and injection of oil throughthe oil wells IIIA. etc. A multielectrode exploring probe |23 is provided with two equipotentialprobing electrodes |24 and |25 and two'current vflow line probing electrodes |26, |21 which make contact with the conducting pool. The exploring probel2l is rotatably supported at one end ofla supporting device |28. A mapping device'llt. rotatably supported at the other end of the supporting device, has tracing points |32. ISI by means of which current ilow lines may be indicated on the isopachous map.

'rnesupportmg device m' ,consists of braces su which support a beam III, a sliding table Ill which is mounted on the beam I in such fashion thatit may be moved along the length of the beam,` and a cross member |40 which in turn ismounted on a sliding table |38 at right angles to the beamand is 'free to slide lengthwise across the sliding tableA at right angles to the beam. The exploring probe and the mapping device are also connected together by means of a shaft |42 and worm and pinion gears I so that rotational movement of the mapping device about its verti. cal axis Vcorresponi'ls to rotational movement of the exploring probe v aboutits vertical axis. A phase-sensitive reversible induction motor IIC mounted on the sliding table is geared to the shaft |42 by means of'a worm gear i to provide means for rotation of the exploring probe and the mapping device under automatic operating conditions. A knob is also provided on the end of the shaft |42 topermit rotation of this shaft when the motor I is disengaged and Y the apparatus isoperated manually. A cabinet |52 contains a direction ampliner, a time-scale amplliler, a.l phase-sensitive induction motor (which operates a calibratedtime-scale dial Il) a timescale totaling device and a revolution counterall of which are employed for automatic operation ofthe instrument. 'Ihe time-scale dial,

` located on the front of the cabinet |52. is calibrated in. time units derived from the reciprocal of the voltage drop across the currentilow line electrodes |20,4 |21. y 'Ihe shaft of the dial IM is an extensionofv the shaft of a rheostat located inside the cabinet |52. lThis rheostat forms part of a balancing circuit so designed vthat for a reascnable range of voltage between the ilow line electrodes |20; |21, the movement of the sliding arm of .the rheostat required for achieving balance is very nearly proportional to the change in the reciprocal of the voltage differential between electrodes |28,` 1 |21. For manual operation a `galvanomet'er llt is connected across the equipotential probing electrodes |24, |25v to indicate when these electrodes are located at points of equal electrical potential in the conducting pool As noted above. Figs. 4 and 6 show the reducedscale model |10 and isopachous map iM, respectively. Both'kare constructed to the same scale and thecontour lines ill of the map Ill are re- `lloililetl Nationally in the model lll. l0 that depth of the conductingpool ||2 at any point corresponds to the oil content of the oil-bearing formation at the corresponding location. The oil wells ||8 indicated on the isopachous map are represented in the model by the metallic xed electrodes |20.

Fig. 5 shows the laminated type of construction of the model l| |0, which is constructed of several layers of plywood. -Each layer has had removed from it a sectiona1 area corresponding to a contour line of the map. The individual layers are fastened together and the bottom of the conducting pool ||2 is coated with wax |58 so thaty the sides and the bottom of the pool have a smoothly graduated slope. The electrode |r is inserted into the pool through a hole drilled in the bottom of the model. A wire lead |160 connected to the lower end of the electrode |20 is run along the bottom of the model for connection of the electrode with the current control unit |22. The pool or basin is lled with an electrically conducting dilute aqueous solution |62 of an electrolyte, which represents the oil content of the oil-bearing formation.

Fig. 7 shows details of the exploring probe |23, the supporting device |28, and the mapping device |30, already referred to in connection with Fig. 3. The exploring probe has a rotatable vertical shaft |64 supported from the cross member |40. An exploring foot |66 attached to the lower end of the shaft |64 comprises an insulation block |68 of a. material such as a phenolic condensation product, i. e. machined Bakelite, in which four tungsten rods (which constitute the probing electrodes |24, |25, |26, |21) are mounted. These electrodes are disposed at the four corners of a rhombus, the equipotential electrodes |24, |25 lying on one diagonal and the current flow line electrodes |26, |21 lying on the other diagonal. The axis of the current flow line electrode |26 is the same as theaxisof the vertical shaft |64, so that upon rotation of the exploring probe |23 the other three probing electrodes move in circular paths around the electrode |26. Wires |10 attached to the tops of the four probingl electrodes are connected respectively to slip rings` |12. Brushes |14 contacting the slip rings are provided in order that electrical connections may be made to the probing electrodes without danger of tangling and breaking the connecting wires.

The mapping device |30 has a rotatable vertical shaft |18 supported from the cross member |40. The lower end of the shaft |18 forms the tracing point |32 and is tapered to a slightly blunted or ball-shaped point to allow it to slide over the surface of the map. A cross member |82 is slidably connected at one end to the lower portion of the Shaft |18 so as to permit vertical movement thereof. This portion of the shaft |18 is grooved to receive a lug or key |84 on a cross member |82, thereby preventing rotational movement of the cross member |82 with respect to the shaft |18. The other end of the cross member |82 supports the sharp tracing point |33. A spring |86 held in place on the shaft |16 by a collar |88 is provided to maintain the normal position of the tip of the tracingv point |33 slightly above the surface of the map. A springtype push button switch |30 positioned on the shaft |18 is provided to push the sharp tip of the tracing point |33 into the surface of the map during Opz-ration of the apparatus and at the same time make an electrical connection at its contact point |8| for operation of a time-scale l0 e gitaligg device described later in connection with g. 1

The position of the exploring probe |23 in relation to the model ||0 and the position of Ithe mapping device |30 in relation to the map ||4 are always identical, due to the construction of the supporting device |28. 'I'he main support beam |36, which is laterally grooved on both sides.` is maintained in a fixed positionby means of the braces |34 shown in Fig. 6. The sliding table |38 has a recess shaped to conform to the cross section of the support beam |36 and is free to move laterally with respect thereto. The sliding table |38 also has another recess shaped to conform to the cross section of the cross member |40 and in which that cross member is free to slide laterally at right angles to the support beam |36.

The shaft |42, which connects the exploring probe and mapping device by means o'f the identical worm and pinion gears |44, isfrotatably supported by bearings |82 in brackets |84, which arel mounted on the cross member |40. By adjustment of the worm and pinion gears. the relative position and direction of the transfer points |32, |33 is made to coincide Iwith that of the current flow line electrodes |26, |21. Upon rotation of the shaft 42, either manually by means of the knob |50, or automatically by means of the motor |46 shown in Fig. 3, the exploring probe and the mapping device rotate simultaneously, the relative position and direction of the transfer points with respect to the electrodes 26, |21 being identical for any angle of rotation.

Fig. 8 shows the electrical circuit for manual voperation of the apparatus. Current is supplied -the conditions of the problem. By choosing between sockets 208 and 2| 0, into which one end of the plug-in resistor may be inserted, the phase of current flowing through any fixed Aelectrode may be selected, and the electrode may' be made to represent either an injection or extractionwell. The other end of the plug-in resistor is inserted in a socket 2|2. A rectifier type voltmeter 2|4 is provided for connecting across the precision resistor 204 of any electrode circuit by means of a selector switch, not shown, in order that the voltage drop across the precision xed resistor may be measured and the magnitude of the current flowing in that circuit determined.

The equipotential probing electrodes |24. |25, are connected to a. galvanometer |56, which is of the null incidating type and serves to show whether or not the equipotential electrodes are located at points of equal potential in the conducting pool.

The current flow line electrodes |26, |21 are connectedA to a time-scale balancing circuit so that the voltage differential across these elec# trodes is in opposition to a fraction of a standard voltage supplied by an autotransformer 2|6 and a transformer 2|8. The input side of the autotransformer 2|6 is connected to the output side of the autotransformer |86, which regulates the voltage supply in the current control unit. By using the voltage supply for the current control unit as the source of the standard voltage, the current supplied to the nxed electrodes of the y position the voltage drop acrossthe resistance 226 is ,equal tov the voltage -diierence between the electrodesL |26, |21-; Themovement of the sliding r` arm oi' the rheostat 222 required `to obtain this voltage drop acrossthe resistance 226 is approxia mately proportional to the change inthe reciprocal offthevoltagedifference between the electrodes |26, |21. The time-scale dial |64 is at tached tothe axis of the sliding arm of the rheo. stat 222 by` a shalt, 226, so that the degreer of rotation ofthe sliding arm,v and therefore kthe amount of resistance placed in the `standard voltagecircuit by the rheostat 222 is indicated by arbitrary calibrations on the dial. Since ythe f distance betweenthe electrodes |26, |21 is very small as compared to thefdimensions 01.1 the conducting. pool ||2, the voltage difference between these electrodes may be considered to be a measure loi' the potential gradient along a currenti'low line ,and this potential gradient may be presumedk t be essentially constanty atall Points between these electrodes. Since potential gradient in the conduction model is analogous to pressure gradient'in the corresponding iluid ow system, and` since lthetime 'required fora unit ofiluid to traverse an incremental length' oi'v iow line is proportional to the reciprocal of the pressure gradient, the reciprocal koi! the voltage differencey between .the electrodes |26, |21 is proportional, to the'transit time of an element of fluid along the equivalentincremental -length of ilow line inthe iiuid ilow system. The calibrations on Vthe Y dial |54 therefore represent transit time for the` ijlowoi `fluid in the cil-'bearing formation in arbi- 12 the particular case illustrated by Fig. 9, the'direction amplifier consists of a single voltage ampliilcation stage resistance coupled to a driver' stage which in turn is transformer coupled to a power ampliilcation stage consisting of ltwo 61.6 tubes in push-pull class B operation. The output o! the amplifier is applied to the shading pole windings ofthe; phase-sensitive induction motor |46 through an impedance matching transformer contained inthe amplifier. In the motor |46 (which Ais of the reversible shaded pole induc- Y tion type capable ot operation as a 2 phase motor) excitation of the main lileld windings is obtained by a 110volt. 60 cycle power supply and excitation of the two sets of shading coils is obtained by means of the output of the direction amplifier 223. When the shading coils are connected in series the direction of rotation of the motor |46 depends on the relationship of the phase oi' the currents in the mainexisting ileld and in the shading coils. vIt a difference in potential exists between the equipotential probing electrodes, this potential diilerence is ampliiled and applied to the shading coils of the servo-motor. As a result the, armature of the motor |46 rotates. This causes rotationvof the exploring probe |23 in a direction'tending-'to reduce the difference in potential` between the equipotential electrodes.

. When an equipotential state is reached no vsignal is applied tothe amplier and no excitation is applied to the shading coils, sothat no further rotation of the motor takes place. Because of the mechanical linkage between the exploring probe |23 and the mapping device |36, rotation oi' the latter is obtained simultaneously so that when a state o! equal potentials` is 'reached for the equipotential' electrodes, the position of the transfer points |32, .|33 with respect tothe map corresponds to the position of the iiow line'electrodes |26, |21 with respect to the model.

Operation oi the calibrated time-scale dial |64 may also be carried out automatically by replacing the galvanometer `224 of Fig. 8 by a time# trarytime-scale units which are inversely propor-r tional to thetotal current supplied to the model,r

scale amplier 230 and providing a time-scale phase-,sensitive inductionmotor 232 to simultaneously' operate the sliding arm of the rheostat 222 and the Atime-scale dial |54. Any amplifier capable ofvhandling a cycle signal without introduction of excessive harmonic or phase disand consequently'to the total rate of ilow of fluidA in' the formomm.` The position or the'ourrent iiow line electrodes |26, |2'|- with respect to the.

y conductingpool is recorded on the isopachousl map of the yformation by means of the mapping devicev andallne connecting the two points indicated on the map by the vtracing points |32, |33 represents thevportion Lof the currentl ilow line for which rthe transit time is determined bythe readingr obtained on the time-scale dial.

Fig. 9 shows an electrical circuit for fully auto-` y matic operation y'of the instrumentof Fig. 3r et seq. The circuits for the current control unit |22 and thevtime-scalebalancng circuit for de.-k terminingl the kpotential diierence between the electrodes |26, l|21 are the same as described in connection with Fig.` 8 for `manual operation.

The exploringprobe |23 maybe made to automatically seek points of equal potential forthe probing electrodes |24, |26 by replacing the gal-4 vanometer |56 with a direction amplier 226,

which detects and ampliiles anyvoltage diilerence existing'between these equipotential electrodes.

' ArLv amplifier capable of handling Aa 60 cycle' signal without vintroduction of excessive harmonicV or phase distortion and having suillcient power out-` put to operate the motor |46 may beused. In

wrtion andhaving sumcient power output to operatethe motor 232 may be used. Fundamentally, the construction of the time-scale ampliileruisdike that of th direction ampliiler 223. The output of the ampliiier 236 supplies power to the shading pole windings of a time-scale motor 232 through an impedance matching transformer contained in the amplifier.y

UAshaIt' 234 connects the sliding arm of the rheostat 222 lwith the shaft 'of the motor 232, so that rotation of ythis motor determines the amount of resistance placed in the balancing circuit by the rheostat. If the fraction of the .standard voltage opposing the voltage diiference across the `electrodes |26, |21 isnot exactly equal to this voltage diierence,vthis inequality is applied tothe amplier 236 and the amplined signal in turn operates the motor 232in a direction tending toreduce the inequality in voltages. Thus the sliding arm oi' the rheostat 222 is moved to a Vposition which will place in the balancing circuit the exa-ct yresistance required vfor voltage balancav The calibrated time-sone dm |54 is mounted on the shaft 236 (which in turn is connected to tlieshaft of the motor 232) so that the dial rotates simultaneously and in accordance with the 13 sliding arm of the rheostat 222, thereby indicating'in arbitrary time units the position of that sliding arm.

The process of manually recording and totaling all of the time-scale readings observed on the calibrated time-scale dial for thenumerous individualoperations required for establishing each current line charted during the `operation of the apparatus may be eliminated by employing a time-scale totaling device 238 and a `revolution counter 248. 'Ihe former is connected by a shaft 242 to the time-scale dial |54 and is controlled by the position thereof. l K

Details of the time-scale totaling device are shown schematically in Fig. l0.` Referring to this figure. a cam 244, mounted on a shaft 242 is driven by the time-scale 232, and is so shaped that the yangle through which a feeler arm 246 must advance from its'initial zero position to touch the cam 244 is directly proportional to the 14 turn deenergizes the coil 288 of the relay 214. opening the'contacts 268, 288.

During the return of the feeler arm to its zero position, the counter ratchet 266 slips and theV maps are themselves constructed from informareading of the time-scale dial r,|54 rthroughout f the entire scale. The feeler arm is provided at each end with insulated electrical `contact pins 248, 268 and is coupled by a friction drive bear-v ing 252 to a shaft 254, which in turnlis coupled through a suitable gear trainl 256 tov a shaft `258, and by means of a disengagingtypecoupling 258 to a reversible induction motor-' 268.A 1 The shaft 258 of the motor 268 is also coupled through a suitable gear train 262 toal shaft2`64 which drives the revolution counter-.248v` through a ratchet 266 -so that the dials of the counter. advance on the forward stroke of the feeler arm toward the cam, but are undisturbed onthe reverse stroke of the feeler arm to its original or zero position. The dimensions of the'cam and the feeler arm are so chosen in conjunction with the gear train 256 and the shaft 264 that -an advance of the feeler arm of approximately two degrees corresponds to one revolution of the shaft 264 and hence to one time-scale unit as recorded by the revolution counter. 1

The power for operation of the time-scale totaling device is obtained from a 110 volt supply by means of a step-down transformer 268 which supplies the power to operate thereversible induction motor 268. A battery 218 'is also provided to supply current for actuation of relays 212, 214. Y

Operation of the totaling device is started by closing the contacts of the push button |98 located on the mapping device I 38. This completes the energizing circuit of a coil 216 of the relay 212, thereby closing contacts 218, 288, which are locked into position by a locking key 282.

The power circuit for operation of the motor 268 is completed through the contact 288 of the relay 212 and a contact 284 of thel relay 214. Then the feeler arm 246 advances until it touches the cam 244. When contact is made with the cam, the circuit for energizing the coil 266 of the relay 214 is completed, causing contact 284 to open and the contacts '288 and 288 to close.

Opening of the contact 284 breaks the power circuit for the forward, operation of the motor 268 and the closing of the contact 288 completes the power circuit for -reverse operation of the motor v268, thus returning the feeler arm to its original zero.` position. Closure of the contact 298 insures energization of the coil 286 and serves as a lock to keepthe contact 288 in the make position.

Whensthe feeler arm returns'to its zero posir tion,contact of the pin 258 with a grounded contact 292 momentarily completes the circuit for energization of a releasecoil 284 of the relay 212. causing ,the contacts L218, 288 to open. This in tion derived from geological surveys of the producing area. The outline of ,the map corresponds to the geometry of the formation and the volume of oil or gas at various locations in the formation is indicated on the'map by contour lines ||6 for definite increments of volume. In the preparation of the model the horizontal geometry of the conducting pool is made to correspond with that of the map. The vertical geometry is arbitrarily established by making each layer of plywood correspond to one or more contour lines and theresulting reduction in scale as compared to the actual formation is greater in the horizontal plane than in the vertical plane. The completed model is placed inv position under the exploring probe and the leads from the fixed electrodes representing wells are connected to the current control unit. The isopachous map is correspondingly placed in position under 'the mapping device. The conducting pool ||2 is lled with a dilute aqueous solution of an electrolyte such as copper sulfate or other ionizable salt. The exact concentration of salt in the solution is not critical but the conductivity of the solution should be low in order that the potential drop between the current ow line electrodes |26. |21 will be of an easily measurable magnitude a low current densities.

The electric currents passing through each electrode are adjusted in direct relationship to the rates of extraction or-injection of fluid in the corresponding oil wells. Adjustment of the individual currents passing through each electrode is obtained by means of the variable resistors 282 and the fixed plug-in resistors 286. By selecting between the terminals 288, 2|8 for f the fixed plug-in resistors 286 it is possible to exploring probe |28 is placed at the desired starting point, ordinarily adjacent to one of the xed electrodes |28, by moving the sliding members of the supporting device.

For manual operation of the instrument, the exploring probe is rotated by turning the knob |58 until the galvanometer |56 connected to the exploring electrodes |24, |25 (i. e. theequipotential electrodes) registers zero. The rheostat 222 is then adjusted by .means of. the knob of the time-scaley dial |54 until the galvanorneter 224 registers zero. The inverse of the difference in potential between the flow line electrodes |26, |21 is then read as arbitrary time unitsl from calibrations of the time-scale dial |54. The sliding members of the supporting device.|28 are then moved so that the tracing point |32 occupies with the former position of the other tracing point |83. and the process is repeated until a current line is traced out on the isopachous map asfar as desired. For each operation the readon Fig. 8)

- l ing of the calibrated time-scale dial |34 is Vrecorded andthe sum of the individual values corresponds to `the total transit time of an element of-,ilu'id along a corresponding path inthe formation. A permanent record of each current line u obtained by drawing arcurve throughthe vindividual points mapped out `by the tracingl poma m. un

s u an' uopoenous mop or o wet gos seid 4having an inlectlon well H3A and three exy wells ||3B, H3C, IIOD. 0n it have been plotted a numberfof flow lines obtained for' an assumed drygas inputrate at the injection Vwell and assumed extraction rates of wet gas at the other. wells. Each flow line is obtained by -pnomg me sow une e1eetrode m of the exploring probe clos'e to' the electrode |20 corresponding i 'to the injection well, the tracing point |32 occupy- 'ing a corresponding position on the map. The

apparatus is then permitted to seek the equi- @potential line, with the resultv lthat the `tracing point |33 rotates'about theother tracing point to locate a point on `the ilow line, i. e. a line normal to `the .equipotential line. The button |33 is then pushed down so that the tracing point |33 marks the'chart. Then the probe and the marking device are moved `so` that the tracing point .|32 is on themark made by the point |32,

and the operation is repeated. f Each time it f is repeated obtained. l

-As each flow lineis traced, the corresponding is noted by theA time-scale totalizer, thev accumulated transit times is noted yat e'achipoint along the flow line. After the series of flow lines are plotted, with transit timesnoted at pointsalon'g each line, points of equal transit time en the several lines `are* joined by cross 'lines v(indicated asfDry'Gas IInvasion Fronts Each* such invasion'front shows the extent of dry gas penetration into the held after a'given time-interval for the assumed extraction and Ainjection rates. It will be noted that the reached the well H3C, indicating` break through." 1 This means that the extraction rate 1 edfor the *wenk Hacjs too high in relation :oth-ooe assumed for wens Ilan and mn, for the 'rates should vbe such that break through is :accomplished simultaneously for each well. To 'assure'optimum production from the tleld, ilow lines and invasion fronts should be plotted again with new assumptions, until -break through" occursV simultaneously i at all three extraction Moreover, the results 4plotted on Fig. 6

showthat a fourth extraction well should be placed in the fleld at orabout position 333 in order to assure proper recovery from this portion of the neld. f i

As already'mentioned, various operations can be carried out automatically. For example, the rotation `of the exploring probe f |23: can be achieved automatically by means. of.y the motor |53 operated by the direction amplifler223. The

balancing of the rheostat n: een be performed automatically by meansof the motor 232 operated by the time-scale lamplifier 233. By means of the time-scale totaling device 233y and the revolution counter `23|), time-scale units for any specilied interval along4 a current ilow -line may be computed automatically as the current flow line In automatic operation the exploring probe will rotate to obtain a position such that no po- Aa newv point on the flow line isv 1sy electrodes |24. |23.'

plied tothe direction ampliiler 223 and the ampliiied voltage is `applied to the shading coils of the motor |33 to caus'e'rotation of the motor ln a direction suchthatthe exploring probe is turned to a position where no diiferencein potential occurs" between. the equipotentialf probes. During the "time the exploring foot or probe vis thus oriented, the time-'scale balancing circuit is also seeking a balance throughthe adjustment of the rheostat 222, and the rheostat .will come-to rest shortly after thedirsction system has reached a balance. This is achieved through the potential balancingcircuit and the time-scale ampli'iler 233 and the motor 232..v` 'Asf long asl the fraction of 1 the l standard f voltage, ,supplied from the trans- 4former4 2I3 in oppositiony to the potential differencefbetween the `flow line electrodes |23. |21

does not .exactly balance this potential dif- .,ference,jthe diilerencef inl voltage is rapplied' to the time-scale amplifier 233. where it isamplied, the amplifledfvoltage being applied to the shading coils of` the motor 232. This results in .the rotationof that motor in a direction to rotate the sliding arm of the rheostat 222 to a position where thefapplied fraction of standard voltage exactly balances the potential difference between the flow lineelectrodes |23, .|2I. With both direction and time systems at balance` the instrumentindicates both the direction of the currentflow line by the angular position of the exploring vfoot and the equivalent transit timeacro that section'of 4 contacts |3l, which cause thetime-seale totaling 'lower'f' or the two invasion fronts plotted has flow line by the reading of the calibrated timescale dial III.' This infomation Vmaybe recorded by pressing the push button |33 on the mapping device l33. This simultaneously depresses the tracing point |33 to make a punch mark on the isopachous` map and also closes the electrical device 233 to-register on` the counter '233 the time 'units indicated by the time-scale Ill. The relation of the arbitrary time-scale units indicated` by the apparatus and the time of flow of fluid through the oil-bearing formation is a function -of the relationship of the current applied to the l ilxedelectrodes |23 with respect to the ow rates of uid in and out of the formation through'the j'times desirable to provide two or even more time tentiai difierence exists between the equipotentiaL unit scales to achieve greater accuracy in determining transit time values. l

In the operation of the apparatus of Figs. 3 to 10 inclusive, as described above, flow lines 'and flow" ratesare obtained directly,.and the equipotential lines are not recorded.` 'I'his practice is followed because, in oili'leld studies 4the equipotential lines'usually are not relevant. However, in other engineering problemsthe shape and lo'- cation of equipotential lines may be important, audit is a simple matter to record them. Thus as shown in Iilg- 8, the leadsextending from the eduipotential probes |23, |23 to the'galvanomete'r Aslong as any diilerence in` potential existsbetween these electrodes, it is apv Fig. 1.

It may be desirable to know what the potential is along any particular equipotential line, and this can be determined, as illustrated in Fig. 8, by employing a galvanometer 366 connected between the slider of a potentiometer 361 and one of the exploring electrodes employed to iind the equipotential line, say the electrode |26, the end points of the potentiometer being connected between an "injection electrode and an extractio electrode.

We claim:

l. In a device for determining the condition of a system operating at least approximately in accordance with Laplaces equation, the combination which comprises an electrically conductive body the shape of which is analogous to the system undergoing investigation, means for pressing across the body an electrical potential analogous to the force impressed upon the system, chart supporting means,.a probe member` having at least three electrical contacts spaced from and out of line with each other and adapted to contact the body, means for measuring the potential between one set oi two of the contacts, means for measuring the potential between4 another set of two of the contacts which deiine a line transverse to that deined by the first set, a marker member having a plurality of markers spaced from each other and disposed adjacent the chart, means for' moving the probe member and the marker member in unison to corresponding positions respectively in the body and the chart, means for rotating the contacts on the probe member and the markers on the marker member in unison through corresponding angles, and means for contacting the markers with the chart.

2. Apparatus according to claim 1 provided with a pair oi markers on the marker member sodisposedthatalinedrawnbetweenthemis oriented with respect to chart in the same way that a pair of contacts on the probe member are oriented with respect to the body.

3. Apparatus according to claim 1 provided with a pair of markers on the marker member which are oriented on the chart at right angles to the orientation of a pair of` contacts on the probe member with respect to the body.

4. In a device for determining the condition of a force system operating at least approximately in accordance with Laplaces equation and having an electrically conductive body the shapeA of which is analogous to the system and means for impressing across the body an electrical potential analogous to the force impressed upon the system, the combination which comprises chart supporting means, a rotatable probe member having at least three electrical contacts spaced from and out of line with each other and arranged to contact the body, one of the contacts y 18 spaced from each other and disposed adjacent the chart with one of the markers disposed on the axis of rotation of the marker member, means for contacting the markers with the chart, means for moving the vprobe member and the marker member in unison to corresponding positions respectively on the body and on the chart and means for rotating the probe memberand marker member in unison through corresponding angles.

5. In a device for determining the condition of a system operating at least approximately in accordance with Laplaces equation and including an electrically conductive body analogous in shape to the system and means for impressing across the body electrical potential analogous to force impressed upon the system, the combination which comprises a chart supporting means, a rotatable probe member having at least three contacts spaced from each other and disposed to contact the body in a pattern which deiines a right angle, means for measuring the potential between a irst set of two of the contacts, means for measuring the potential between another set of two of the contacts which deilne a line at right angles to that deiined by the iirst set, a rotatable marker member having two markers spaced from each other and disposed adjacent the chart, means for moving the probe member and the marker member in unison to corresponding positions respectively on the body and on the chart, means for rotating the probe member and the marker member in unison through corresponding being disposed on the axis of rotation of the probe member, means for measuring the potential between a first set of two of the contacts, means for measuring the potential between another set of two of the contacts which define a line transverse to that dened by the iirst set, a rotatable angles and means for pressing the markers against the chart.

determining dynamic 6. In apparatus for characteristics of a steady state system upon which forces operate. the combination which comprises an electrical model of the system including anelectrical conductor analogous in shape to the system and means for impressing thereon electrical currents analogous to forces acting uponthe system, a chart of the system, a probe' member having two electrodes rotatable about a common axis to positions of equipotential on the conductor, means for measuring the potentials between the two electrodes, an auxiliary electrode mounted on the probe out of line with the iirst two electrodos but rotatable about the same axis, means connected to the auxiliary electrode for measuring potential gradient in said conductor along a current iiow line transverse to the line joining the iirst two electrodes and passing through the auxiliary electrode, a marker member having at least two markers spaced from each other contaetable with the chart and rotatable about a common axis and means for moving and rotating the marker member and the probe member simultaneously and in synchronism with each other so -thatthe markers locate on the chart a line corresponding to that on the conducwr along which the potential` gradient is ber having two'electrodes rotatable about a common axis to a position of equipotential on the conductor, means for measuring the potentials marker' member having a plurality of markers 75 between the two electrodes, means connected to 19 the Vpotential measuring means for `automatically rotating the electrodes to the position of equipotential, an auxiliary electrode mounted on the probe out of line with the ilrst two electrodes but rotatable about the same axis, means coni ynected .to'the auxiliary electrode Vfor measuring .potentialngradient -in said conductor along a current dow line normal to the line ioiningthe first two electrodes vand through the auxiliary electrode, a marker member having at least two markers spaced from each other contactable with the chart and rotatable on a common axis and means for moving `and rotating the marker member and the probe member simultaneously and in synchronism with each other so that the,

markers locate on the chart a. line corresponding' to that on the conductor along which the potential gradientis measured.

8. In apparatus for determining dynamic characteristics of a steady state system upon which forces operate, the combination which comprises an electrical model o! the system including an electrical conductor analogous in shape to the 'system and means for impressing thereon -elec'- trical currents analogous to forces acting upon the system, a chart of the'system, a probe member having two electrodes rotatable about a common axis to positions of equipotential on the conductor, means for measuring the potentials between the two electrodes. an vauxiliary electrode mounted on the head out of line with the first two electrodes but rotatable about the same axis.

means connected to they electrode for measuring the reciprocal of potential gradient inthe conductor along a current ilow line psing through the auxiliary electrode and transverse to a line joining the rst two electrodes.' a marker member having at least two markers spaced from each other contactable with the chart and rotatableY about a common axis and means for moving and rotating the marker member and the probe member simultaneously and in synchronism with each other so that the markers locate on the chart a line correspondingto the current ilow line on the -conductor along which the potential gradient is measured. n

9. In apparatus for determining dynamiccharmarkers'locate on the chart a line corresponding 20 characteristics of a steady state which .forcesoperate the acting upon the miem. a chart ofA the system, a

probe memberha'ving two electrodes rotatable about a common axk to positiom of equipotential on the conductor, meam` for measuring the 'potentials between the two electrodes, electrode means mounted on the probe at rightfangles to the two electrodes and rotatable therewith about the same axis, means to theelectrode means for thel potential gradient in the conductor along a ein-rent now line at right angles to that between the two conductors. a marker member having atleast two markers spaced from each other contactable with the chart and rotatable about a common axis and means` for moving and rotating the marker member and the probe member simultaneously and in synchronism with each other so that the to that on the conductor along which the potential gradient is determined.

l1. In apparatus for determining the progress oftheinteriacebetweenauidinplaceina porous body and an invading fluid. the combination which comprises a conductor analogous in shape to the body, means for impressing across the conductor current analogous to the rate of means linked to the probe for plottingon a chart ofthe body the line along which the potential gradient is determined.

12. In apparatus for determining flow of petroleum in a petroleum-bearing formation comacteristics of a steady state system upon which forces operate, thev combination which comprises an electrical model oi' the system including an electrical conductor analogous in shape to the system and means for impressing thereon electrical currents analogous to forces acting upon the system, a chart ot thesystem, a probe member having two electrodesrotatable about a common axis to positions oi equipotential on the conductor. means for measuring the `potentials between the two electrodes. means mounted on the head and rotatable about the same axis as the tlrst two electrodes for locating a line in the conductor transverse to that passing between the first two electrodes, means for measuring the reciprocal of potential gradient along the line located by said means., a marker member having at least two markers spaced from each other con\ tactable with the chart and rotatable about a common axis, means for moving and rotating v the marker member and the probe member simultaneouslyy and in synchronism with each other y so that the markers locate on the chart a line corresponding to that on the conductor along which the reciprocal of potential gradient is measured, and means i'or adding a serias of said reciprocals measured with the probe at diierent points in the conductor. l I

10. In apparatus for determining dynamic prising a model of the formation in which the petroleum content of the formation is represented by a pool of electrolyte and in which production and injection wells are represented by electrodes positioned in theelectrolyte, the combination which comprises an exploring probe having at least three electrodes in ilxed geometrical relation to each other and arranged to contact the pool, means for moving the probe with respect to thepool, means for rotating the ilrst two ot the electrodes ofthe probe on a common axis to pointsA of equal electrical potential in the pool, means including the'third electrode of the probe for measuring potential gradient in the pool along a current flow line at right angles to a line drawn through lines of equal electrical potential located by the rst two of the electrodes, a

mapping device. means for moving the mapping devicel and the probe simultaneously to corresponding positions. coupling means for obtaining simultaneous rrotation of the probey and the mapping device, means for measuring the reciprocal .of the `potential gradient and means for totaling rthe reciprocal obtained at ve positions of `said probe along the current now lines.

13. In a device for determining ilow characteristics ot petroleum in a petroleum-producing formation comprlsing a reduced *scale model in which the petroleum contento! the' formation is represented by a pool of electrolyte and in which production `and injection wells' are represented by electrodes located in said pool, the combination which comprises an exploring probe vhaving two equipotential electrodes and two current `iiow electrodes so disposed that lines drawn through the two kinds of electrodes cross at right angles, means for moving the probev over the pool to bring the electrodes in contact therewith, a mapping device for graphically recording on a map the position of said current ilow electrodes inthe pool, thereby determining a current iiow line, means for moving the probe and the mapping device simultaneously to corresponding positions respectively on the pool and the map, couplingI means for rotating the probe and the mapping device simultaneously and for bringing the equipotential electrodes to a position ot balanced potential in the pool, means for measuring the reciprocal of the potential diilerence between the points of contact of the current ow line electrodes in the pool along the current iiow lines, and means for totaling the reciprocals obtained at successive positions of said `probe along the current ow line.

14. In a device for determining dynamic characteristics of a steady state system. the combination which comprises an electrically conductive body the shape of which is analogous to the system undergoing investigation, means for impressing across the body an electrical voltage analogous to the force impressed upon the system, a probe member having two electrodes movable to positions of equipotential on the conductor, means for measuring the potential between the two electrodes, at leastone auxiliary electrode mounted on the probe in iixed spacial relationship to the other two electrodes, means connected to the auxiliary electrode for measuring potential gradient in the conductor along a line passing through the auxiliary electrode and transverse to that connecting the other two electrodes.

15. In a device for determining dynamic characteristics of a steady state system, the combination which comprises an electrically conductive body the shape of which is analogous to the system undergoing -investigation, means for impressing across the` body an electrical voltage analogous to the force impressed upon the system. a probe member having two electrodes movable topositions of equipotential on the conductor, means including a third electrode mounted on the probe for measuring the reciprocal of the potential gradient in the conductor along aj line transverse to that between the first two electrodes, and means for adding a series of said reciprocals' measured with the probe at successive Points in the conductor along the line.

16. In a device for determining dynamic characteristics of a steady state system, the combination which comprises an electrically conductive body the shape of which is analogous to the system undergoing investigation, means for im- REFERENCES CITED vThe following references are of record in the file oi thislpatent:

UNITED STATES PATENTS Number Name Date 1,825,855 Graig Oct. 6, 1931 1,919,215 Gunn July 25, 1933 2,368,217 Hayes Jan. 30, 1945 2,382,093 Phelan Aug. 14, 1945 2,440,693 Lee May 4, 1948 OTHER REFERENCES Textbook, Electron Optics- Theoretical and Practical, by Myers. l D. Van Nostrand Co., pages 122 to 142, inclusive.

Textbook, Geophysical Exploration, by Heiland. 1940, chapter 10, Pages 681 to 706.

1939 edition published by 

